What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one half that of a freely falling body ? (The densities of metal and of liquid are ρ and σ respectively and the viscosity coefficient of the liquid is η) -

Engineering

Physics

Viscosity

Question

$\frac{r^{2} g}{9 η} (ρ - 2 σ)$

$\frac{r^{2} g}{9 η} (ρ - σ)$

$\frac{r^{2} g}{9 η} (2 ρ - σ)$

$\frac{2 r^{2} g}{9 η} (ρ - σ)$

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$\frac{mg}{2} = mg - B - 6 πηrv$

$\frac{4}{3} {pr}^{3} ρ \times \frac{g}{2} = \frac{4}{3} {πr}^{3} ρg - \frac{4}{3} {πr}^{3} ρg - 6 πhρv$

$6 πhrv = \frac{2}{3} {πr}^{3} ρg - \frac{4}{3} {πr}^{3} σg$

$v = \frac{2}{9} \frac{r^{2} g (ρ / 2 - σ)}{η}$

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